A335956 a(n) = (2^n - 1)*2^valuation(n, 2) for n > 0 and a(0) = 0.

0, 1, 6, 7, 60, 31, 126, 127, 2040, 511, 2046, 2047, 16380, 8191, 32766, 32767, 1048560, 131071, 524286, 524287, 4194300, 2097151, 8388606, 8388607, 134217720, 33554431, 134217726, 134217727, 1073741820, 536870911, 2147483646, 2147483647, 137438953440, 8589934591

Offset

0,3

Links

Table of n, a(n) for n=0..33.

Formula

For n > 0, a(n) = A000225(n) * A006519(n). - Antti Karttunen, Jul 21 2020

Example

a(4) = (2^4 - 1) * 4 = 15 * 4 = 60.
a(5) = (2^5 - 1) * 1 = 31 * 1 = 31.

Maple

a := n -> `if`(n=0, 0, (2^n-1)*2^padic[ordp](n, 2)): seq(a(n), n=0..33);

Mathematica

a[0] := 0; a[n_] := (2^n - 1) 2^IntegerExponent[n, 2]; Array[a, 34, 0]

Prog

(PARI) a(n) = if (n, (2^n - 1)*2^valuation(n, 2), 0); \\ Michel Marcus, Jul 21 2020
(Python)
def A335956(n): return ((1<<n)-1)*(n&-n) # Chai Wah Wu, Mar 17 2023

Crossrefs

Cf. A000225, A006519, A168604.

Sequence in context: A028423 A269912 A042117 * A179885 A217548 A335734

Adjacent sequences: A335953 A335954 A335955 * A335957 A335958 A335959

Keyword

nonn

Author

Peter Luschny, Jul 21 2020

Status

approved